First, warm up some oil in a skillet over gentle heat. Spread a layer of onion evenly on the bottom and season with salt. Let it cook without stirring until the onion becomes very tender and releases a fragrant aroma, which should take about 15 minutes. Next, add butternut squash and garlic to the mix, and season with pepper. Let it cook for another 15 minutes or until the squash starts to soften.
Turn up the heat to medium-high and add chicken stock to the pan. Bring to a boil, using a wooden spoon to scrape off any delicious browned bits. Reduce the heat to low and mix in corn, peas, and rice. Cover and simmer until the rice is cooked, about 10 to 20 minutes. Introduce the shrimp and simmer until they turn bright pink on the outside and are opaque, approximately 5 minutes.
Combine feta cheese, brine, and milk. Allow the feta to melt slightly before serving right away.